Density Functional Calculations of Metal Clusters: Structure, Dynamics, and Reactivity - Metallic Systems: A Quantum Chemist's Perspective - page 299

1 2 1 2 1 2

Cu 2 ( 1 Σ g ) Cu 2 ( 2 Σ g )

+

Cu 2 ( 2 Σ u )

-

1 1

2 1 3

Cu 3 ( 1 Σ g )

-

2 3 2 3

Cu 3 ( 2 B 1 )

Cu 3 ( 1 A 1 )

+

1 1 1

2 3 2 3 2 3

4 4 4

Cu 4 ( 1 A g )

Cu 4 ( 2 B 3u )

+

Cu 4 ( 2 B 2u )

-

5

4 4

5 5

1

3 2

2 1 3 2 1 3

4

Cu 5 ( 2 A 1 ) Cu 5 ( 1 A 1 )

-

Cu 5 ( 1 A 1 )

+

FIGURE 9.9 Ground-state.structures.of.neutral,.cationic,.and.anionic.copper.clusters.with.
up. to. ive. atoms.. (Reprinted. from. Jug,. K.. et. al.,. J. Chem. Phys .,. 116(11),. March. 15,. .4497,.
2002..With.permission.)

C 2v .symmetry.(Figure.9.9)..This.global.minimum.can.be.obtained.from.the.relax-
ation.of.a.capped.triangle.or.a.capped.ring.bond.structure.of.the.heptamer.ground.
state.. For. Cu 8 ,. a. T d . structure. is. found. to. be. only. 0.5.kcal/mol. higher. than. the. C 2v .
structure..This.structure.has.a.cuboidal.cage.form.compared.with.the.more.spherical.
cage.form.of.the.C 2v .structure..The.search.for.stable.structures.of.larger.clusters.is.
increasingly. more. dificult. because. of. the. increasing. number. of. possible. arrange-
ments.for.isomers..We.have.therefore.used.the.strategy.of.capping.smaller.clusters.
or.solid.state.fragments..In.the.case.of.Cu 9 ,.a.starting.structure.for.optimization.can.
be.obtained.by.single.capping.of.Cu 8 .structures.or.double.capping.of.Cu 7 .structures..
The.irst.procedure.was.accompanied.by.extremely.strong.relaxations,.whereas.the.
second.procedure.resulted.in.all.cases.in.Cu 9 .minima..The.global.minimum.has.C s .
symmetry..It.is.derived.from.the.Cu 7 .bipyramid.by.double.capping.of.two.adjacent.
upper.triangles..The.ive-membered.ring.and.the.bond.between.the.capping.atoms.
are.preserved.(Figure.9.10)..A.C 2v .structure.with.a.slightly.higher.energy.of.1.1.kcal/
mol.is.obtained.from.double.capping.of.adjacent.upper.and.lower.triangles..The.C 3v .
isomer.of.Cu 9 .depicted.in.Figure.9.10.was.obtained.from.the.relaxation.of.a.crystal.
fragment..The.average.bond.distance.of.this.isomer.is.similar.to.the.C 3v .isomer.of.
Cu 7 .and.is.still.considerably.shorter.than.the.bulk.distance.of.2.56.Å.
The.strategy.of.capping.leads.to.stable.structures.also.for.Cu 10 .clusters..The.global.
minimum. has. D 4d . symmetry.. Like. the. global. minimum. of. Cu 8 ,. this. structure. is. a.